A Characterization of the Semantics of Logic Programs with Aggregates

The aggregates have greatly extended the representation power, in both theory and practice, of Answer Set Programming. Significant understanding of programs with aggregates has been gained in the last decade. However, there is still a substantial difficulty in understanding the semantics due to the nonmonotonic behavior of aggregates, which is demonstrated by several distinct semantics for aggregates in the existing work. In this paper, we aim to understand these distinct semantics in a more uniform way. Particularly, by satisfiability, rationality and consistency principles, we are able to give a uniform and simple characterizations of the three major distinct types of answer set semantics.